3.2 Classification of time series

A ts can be represented as a set

\[ \{ x_1,x_2,x_3,\dots,x_n \} \]

For example, \[ \{ 10,31,27,42,53,15 \} \] It can be further classified.

3.2.1 By some index set

Interval across real time; \(x(t)\)

• begin/end: \(t \in [1.1,2.5]\)

Discrete time; \(x_t\)

• Equally spaced: \(t = \{1,2,3,4,5\}\)
  
• Equally spaced w/ missing value: \(t = \{1,2,4,5,6\}\)
  
• Unequally spaced: \(t = \{2,3,4,6,9\}\)

3.2.2 By the underlying process

Discrete (eg, total # of fish caught per trawl)

Continuous (eg, salinity, temperature)

3.2.3 By the number of values recorded

Univariate/scalar (eg, total # of fish caught)

Multivariate/vector (eg, # of each spp of fish caught)

3.2.4 By the type of values recorded

Integer (eg, # of fish in 5 min trawl = 2413)

Rational (eg, fraction of unclipped fish = 47/951)

Real (eg, fish mass = 10.2 g)

Complex (eg, cos(2 \(\pi\) 2.43) + i sin(2 \(\pi\) 2.43))